Sameh S. Daoud

A new RSA vulnerability using continued fractions

Let (n = pq, e) be an RSA public key with private exponent d = ndelta, where p and q are large primes of the same bit size. Suppose that po ges radicn be an approximation of p with |p - po| les 1/8nalpha, alpha les 1/2. Using continued fractions, we show that the system is insecure if delta < 1-alpha/2. Our result is deterministic polynomial time and an extension of Coppersmiths result on a factorization.

A randomized algorithm for determining dominating sets in graphs of maximum degree five

The paper is devoted to demonstrating a randomized algorithm for determining a dominating set in a given graph having a maximum degree of five. The algorithm follows the Las Vegas technique. Furthermore, the concept of a 2-separated collection of subsets of vertices in graphs is used. The suggested algorithm is based on a condition of the upper bound of the cardinality of a local dominating set. If the condition is not satisfied, then the algorithm halts with an appropriate message. Otherwise, the algorithm determines the dominating set. The given algorithm is considered a polynomial-time approximation one.

Parallel Self-Index Integer Sorting

AbstractWe consider the problem of sorting n integers when the elements are drawn from the restricted domain [1...n]. A new deterministic parallel algorithm for sorting n integers is obtained. Its running time is O(lognlog(n/logn)) using n/logn processors on EREW (exclusive read exclusive write) PRAM (parallel random access machine). Also, our algorithm was modified to become optimal when we use

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\sqrt n

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processors. This algorithm belongs to class EP (Efficient, Polynomial fast).

Interactive visualization system for DES

Integer sorting is a special case of the sorting problem, where the elements have integer values in the range [0,n–1]. We evaluate the behavior and performance of two parallel integer sorting algorithms in practice. We have used Ada tasks facilities to simulate the parallel sorting algorithms on a machine consisting of 4-processors. Both algorithms are based on self-index method on EREW PRAM [3,6]. Also, we study the scalability of the two parallel algorithms and compare between them.